Question

1. letters a sign painter is painting a large “x”. what are the measures of angles 1, 2, and 3?

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle 1 and the given 120 - degree angle are vertical angles, so $\angle1 = 120^{\circ}$.

Step2: Use linear - pair property

A linear pair of angles sums to 180 degrees. Angle 2 and the 120 - degree angle form a linear pair. Let $\angle2=x$, then $x + 120^{\circ}=180^{\circ}$, so $x=\angle2 = 180^{\circ}-120^{\circ}=60^{\circ}$.

Step3: Use vertical - angle property again

Angle 3 and angle 2 are vertical angles. Since $\angle2 = 60^{\circ}$, then $\angle3 = 60^{\circ}$.

Answer:

$\angle1 = 120^{\circ}$, $\angle2 = 60^{\circ}$, $\angle3 = 60^{\circ}$